-uniqueness for elliptic operators with unbounded coefficients in

Abstract: Let be an elliptic operator with unbounded and sufficiently smooth coefficients and let μ be a (sub)-invariant measure of the operator . In this paper we give sufficient conditions guaranteeing that the closure of the operator generates a sub-Markovian strongly continuous semigroup of contractions in . Applications are given in the case when is a generalized Schrödinger operator. [Copyright &y& Elsevier]